Unable to copy objects between versions
I just ran into what I believe is the same issue.

Check the Temp path in both versions' preferences. You probably changed it for the old version in the past but forgot to do this in the new installation. You must use the same path otherwise the clipboard contents won't get shared across versions.

What's happening is that upon copying an object Blender temporarily stores it in a file called copybuffer.blend, found in the temp directory. When the temp path isn't the same in all versions preferences you'll get independent copybuffer files in those  different directories, and each Blender version will only read the files from their respective temp directories.

Here's how to setup the temp directory path:

2.79 and earlier

Temp in File tab of  File > User Preferences



2.8+

Temporary Files in File Paths tab of  Edit > Preferences